Modeling of Middle-Ear Mechanics

Quantitative understanding of the mechanical behavior of the external and middle ear is important, not only in the quest for improved diagnosis and treatment of conductive hearing loss but also in relation to other aspects of hearing that depend on the conductive pathways. Mathematical modeling is useful in arriving at that understanding. The middle ear is of course more than just a mechanical system: it has physiological aspects (e.g., muscle contraction, healing) and biochemical aspects (e.g., gas exchange) that directly affect its mechanical behavior. Even when it is studied only from a mechanical point of view, however, it presents considerable challenges. For one thing, it has a complicated and irregular geometry involving a number of distinct structures encompassing a wide range of sizes. Its overall dimensions are in the range of tens of millimeters but it has important dimensions measured in micrometers (e.g., the thickness of the eardrum). One can go even further down the scale and consider the dimensions of the collagen fibers that are mechanically important in the eardrum. The displacements that one must be able to measure to characterize middle-ear mechanics are as small as nanometers in response to sound pressures but as large as millimeters in response to static pressures. The time scales for the mechanical responses of the middle ear range from tens of microseconds for high-frequency sounds to tens of seconds for changes of static pressure, and even millions of seconds for the mechanical changes involved in development and healing. The challenge of the external and middle ear is increased by the many different tissue types involved with very different mechanical behaviors: bone; fibrous connective tissue, with its collagen, elastin, and ground substance; muscle, both striated and smooth; cartilage, both calcified and uncalcified; and synovial fluid. The mechanical properties of low-density air (in the canal and cavities) and high-density water (in the cochlea) are also involved. This chapter starts by reviewing some background modeling topics: Sections 7.2 and 7.3 discuss some general issues related to the modeling of geometry and of material properties as required for realistic models, while Section 7.4 is a discussion of model verification and validation, including the issues of uncertainty analysis and parameter fitting. (See Funnell et al. (2012) for a tutorial review of the underlying mechanical principles and modeling approaches.) Section 7.5 is a review of models that